The reason why Mulan is a princess was for more diversity so that Asians could have one to relate to. Disney had to really stretch the definition of princess to include her. Mulan's reason is for her amazing act of heroism. If there was at least one legitimately royal Oriental princess then Mulan might not be included. If 2 or more Asian princesses were already included then she almost certainly would not. The reasons why Melody and Eilonwy aren't official is because Melody is from a sequel and the Black Cauldron is an embarrassing bomb that's still a black sheep today.
There is a set of rules that Disney uses for their princess lineup. Must be from a fully animated and original film, be human, play a major role, cannot be from bought properties, and the film must be a hit/have cultural impact. Ariel's sisters are too minor and remain as mermaids the whole time. Still you have a point.